The $n\times n$ imaginary matrix $A$ satisfies $A^\top=-A$, so it is skew-symmetric. The <A HREF="https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/normal-form-for-a-matrix-under-the-unitary-congruence-group/964D0AA8DAC0CDB9079F04331B61859D">Youla decomposition</A> is
$$A=iO\Sigma O^\top,$$
where $O$ is a real orthogonal matrix and $\Sigma$ is a real block-diagonal matrix of the form
$$\Sigma = \begin{pmatrix}
  \begin{matrix}0 & \lambda_1 \\ -\lambda_1 & 0\end{matrix} &  0 & \cdots & 0 \\
  0 & \begin{matrix}0 & \lambda_2 \\ -\lambda_2 & 0\end{matrix} & & 0 \\
  \vdots & & \ddots & \vdots \\
  0 & 0 & \cdots & \begin{matrix}0 & \lambda_{n/2}\\ -\lambda_{n/2} & 0\end{matrix} 
\end{pmatrix}
$$
for $n$ even. If $n$ is odd a row and column of zeroes is appended.